Question

In a two-tailed hypothesis test, the area in each tail corresponding to the critical values is equal to.

Answer 1

In a two-tailed hypothesis test with a significance level of 0.05, each tail of the probability distribution contains an area of 0.025. The alternative hypothesis determines the type of test, and the p-value helps interpret the test results.

Step-by-step explanation:

In a two-tailed hypothesis test, the significance level (commonly denoted as α, or alpha) is split equally between the two tails of the probability distribution. If the significance level is set at α0105 (5%), this would imply that each tail contains 2.5% of the total area under the curve. Therefore, when conducting a two-tailed test with a significance level of 0.05, each tail will have an area of 0.025, representing the critical regions where the null hypothesis would be rejected if the test statistic falls within these areas.

The alternative hypothesis (α013, or Ha) indicates whether the test should be one-tailed (left or right) or two-tailed, and does not contain an equality symbol. In the context of p-value interpretation, a smaller p-value indicates stronger evidence against the null hypothesis, prompting its rejection, while a larger p-value suggests insufficient evidence to reject the null hypothesis.

Answer 2

The equality sign should be present in the null hypothesis during hypothesis testing. In a two-tailed hypothesis test, the rejection region's area in each tail is equal to
`\alpha`. If you choose an alpha of 0.01 then beta will equal 0.99